(a) Assuming the dimensions of the nucleus and atom shown in Figure 2.10, what fraction of the volume of the atom is taken up by the nucleus? -15? b) Using the mass of the proton from Table and assuming its diameter is 1.0 × 10? m, calculate the density of a proton in g/cm3.

Solution Step 1 : (a) Assuming the dimensions of the nucleus and atom shown in Figure 2.10, what fraction of the volume of the atom is taken up by the nucleus Atom is made up of subatomic particles which are protons, neutrons and electrons. Protons and neutrons make the nucleus of atom and the the nucleus is located at the centre of the atom and takes most of the mass of the atom. From the figure, given in the question, we get the diameter of atom and nucleus. Therefore, Diameter of atom = 1 - 5 10 -10m [1 = 1 × 10 -1m] -15 Diameter of nucleus 10 m We calculate the volume of the atom using the formula to find volume of sphere as both atom and nucleus are spherical in shape. Formula to find volume of sphere is : 4 3 V = 3r where, v = volume, r = radius and = 22/7 or 3.1415 radius(r) is twice the diameter(d). Therefore, Step 2: Now, we substitute the values in the formula to calculate volume of atom : -30 3 V = 0.407 × 10 m . Similarly we calculate the volume of nucleus : V = 0.407 × 10 -4m . Now we calculate the percentage of the volume of atom taken by nucleus is : -30 3 From above calculations, we got the volume of atom as 0.407 × 10 m and volume -45 3 of nucleus as 0.407 × 10 m . Therefore, percentage = -15 = 100 × 10 % = 10 13% Step 3 : b) Using the mass of the proton from Table and assuming its diameter is 1.0 × 10 -15m, calculate the density of a proton in g/cm3. Formula to calculate density of a particle : where, = density V = volume m = mass We calculate volume of proton using volume of sphere formula as proton is spherical in shape : 4 3 V = 3r where, v = volume, r = radius and = 22/7 or 3.1415 We know mass of proton = 1.0073 amu. Given, diameter of proton = 1.0 × 10 -15m. Radius is twice the diameter. Hence radius of proton is : -15 = 0.5 × 10 m. To convert in cm : = 0.5 × 10 cm.